invertible

简明释义

英[/ɪnˈvɜrtəbl/]美[/ɪnˈvɜrtəbl/]

adj. 可逆的；倒转的

英英释义

单词用法

同义词

反义词

例句

1.In the second part, we study the structure of feedforward inverse finite automata in general case, and we also discuss the structure of weakly invertible finite automata.

在第二部分中，我们研究了较一般情形下前馈逆有限自动机的结构，并且讨论了弱可逆有限自动机的结构。

2.Are Infinite Dimensional Spheres Invertible?

无限维球面可逆吗？

3.Some striking examples of this are thegroupof invertible linear maps ormatrices, and theringof linear maps of a vector space.

一些引人注目的例子是集团的可逆线性映射或矩阵，和环的线性映射的向量空间。

4.The parameter estimation problem to the invertible vector moving average (ma) model essentially is a matrix spectral factorization problem.

可逆的向量滑动平均(MA)模型参数估计问题本质上是一个矩阵谱分解问题。

5.Then T is an invertible linear operator preserving rank - partial ordering on Sn(F) if and only if there exists an invertible matrix (F) such that where .

刻画了在非负无零因子交换半环上强保持可逆矩阵的线性算子。

6.And then, we have two cases. So, the case where the system is invertible corresponds to the general situation where your three planes somehow all just intersect in one point.

有两种可能，一是方程组可逆，这就是一般情况了，这时三个平面交于一点。

7.Due to derivation is invertible, in this sense, one have already completed the derivation for all 8 important water drive curves.

由于推导是可逆的，从这个意义上说，也完成了全部8种重要水驱特征曲线的推导。

8.The transformation applied to the image must be invertible to recover the original picture.

对图像应用的变换必须是可逆的，才能恢复原始图像。

9.For a system of equations to have a unique solution, the coefficient matrix must be invertible.

为了使方程组有唯一解，系数矩阵必须是可逆的。

10.An invertible function can be reversed to obtain the original input.

一个可逆的函数可以被反转以获得原始输入。

11.The function is invertible if it has a unique output for every input.

如果一个函数对于每个输入都有唯一的输出，那么它是可逆的。

12.In linear algebra, a matrix is invertible when its determinant is non-zero.

在线性代数中，当一个矩阵的行列式非零时，它是可逆的。

作文

In mathematics, the concept of an invertible function plays a crucial role in understanding relationships between variables. An invertible function is one that has an inverse, meaning that for every output, there is a unique input that produces it. This property is significant because it allows us to reverse operations and solve equations effectively. For example, consider the function f(x) = 2x. This function is invertible because we can find the inverse function, which is f^{-1}(y) = y/2. This means that if we know the output (y), we can easily determine the original input (x). The importance of invertible functions extends beyond pure mathematics; they are essential in various fields such as physics, engineering, and computer science. In physics, many laws and principles rely on invertible relationships. For instance, the relationship between distance, speed, and time can be described by the equation d = st, where d is distance, s is speed, and t is time. This equation is invertible because we can rearrange it to find any of the three variables if we know the other two. Thus, if we have the distance and speed, we can calculate the time taken, showcasing the practical utility of invertible functions.In engineering, invertible functions are used in control systems to design feedback mechanisms. For instance, in a temperature control system, knowing the output temperature allows engineers to adjust the heating element based on the invertible relationship between power input and temperature output. This ensures that the system functions efficiently and maintains the desired temperature.Moreover, in computer science, invertible functions are integral to algorithms and data structures. For example, in cryptography, many encryption algorithms depend on the invertible nature of certain mathematical functions. The security of encrypted data relies on the fact that while it is easy to encrypt (apply the function), it is difficult to decrypt (find the inverse) without the correct key. This invertible property ensures that sensitive information remains secure from unauthorized access.However, not all functions are invertible. A function must be one-to-one (bijective) to possess an inverse. For example, the function g(x) = x^2 is not invertible over the set of all real numbers because both -2 and 2 yield the same output (4). To make it invertible, we can restrict its domain to non-negative numbers, allowing us to define an inverse function g^{-1}(y) = √y. This illustrates the importance of understanding the characteristics of functions to determine their invertible nature.In conclusion, the notion of invertible functions is fundamental in various disciplines, providing a framework for solving problems and understanding complex relationships. Whether in mathematics, physics, engineering, or computer science, the ability to identify and utilize invertible functions enhances our problem-solving capabilities and enriches our comprehension of the world around us. As we continue to explore these concepts, we gain deeper insights into the interconnectedness of different fields and the significance of invertible relationships in our daily lives.

在数学中，可逆函数的概念在理解变量之间的关系方面起着至关重要的作用。可逆函数是指具有逆函数的函数，这意味着对于每一个输出，都有一个唯一的输入可以产生它。这个性质非常重要，因为它允许我们逆转操作并有效地解决方程。例如，考虑函数f(x) = 2x。这个函数是可逆的，因为我们可以找到逆函数，即f^{-1}(y) = y/2。这意味着如果我们知道输出（y），我们可以轻松确定原始输入（x）。可逆函数的重要性不仅限于纯数学；它们在物理、工程和计算机科学等多个领域都是必不可少的。在物理学中，许多定律和原则依赖于可逆关系。例如，距离、速度和时间之间的关系可以通过方程d = st来描述，其中d是距离，s是速度，t是时间。这个方程是可逆的，因为我们可以重新排列它以找到三个变量中的任何一个，如果我们知道其他两个。因此，如果我们知道距离和速度，我们可以计算出所需的时间，展示了可逆函数的实际效用。在工程中，可逆函数被用于控制系统的反馈机制设计。例如，在温度控制系统中，知道输出温度使工程师能够根据功率输入与温度输出之间的可逆关系来调整加热元件。这确保了系统高效运行并维持所需的温度。此外，在计算机科学中，可逆函数是算法和数据结构的核心。例如，在密码学中，许多加密算法依赖于某些数学函数的可逆特性。加密数据的安全性依赖于这样的事实：虽然加密（应用函数）很简单，但在没有正确密钥的情况下解密（找到逆）却很困难。这种可逆属性确保敏感信息不被未经授权的访问者获取。然而，并非所有函数都是可逆的。一个函数必须是一对一的（双射）才能拥有逆函数。例如，函数g(x) = x^2在全体实数集上不是可逆的，因为-2和2都会得到相同的输出（4）。为了使其可逆，我们可以将其定义域限制为非负数，从而允许我们定义逆函数g^{-1}(y) = √y。这说明了理解函数特性以确定其可逆性质的重要性。总之，可逆函数的概念在各个学科中都是基础，为解决问题和理解复杂关系提供了框架。无论是在数学、物理、工程还是计算机科学中，识别和利用可逆函数的能力增强了我们的解决问题的能力，并丰富了我们对周围世界的理解。随着我们继续探索这些概念，我们更深入地了解不同领域之间的相互联系，以及可逆关系在我们日常生活中的重要性。